Research
Publications, preprints, and working papers — organised by topic
Affiliation
Combinatorial Commutative Algebra
11 itemsMy core research area: polyomino ideals, Cohen–Macaulay posets and cells, intersection cohomology of fans, and lattice theory of rational fans — the algebra hiding inside combinatorial and geometric objects.
1
Geometric Localization of Relation Lattices
Rizwan Jahangir, Daisuke Ishii
2
Intersection Cohomology and Canonical Lattices on Toric Varieties: A Local-to-Global Combinatorial Framework
Daisuke Ishii, Rizwan Jahangir
3
Canonical Lattices and Integer Relations Associated to Rational Fans
Rizwan Jahangir
arXiv:2601.05678
4
On Cohen–Macaulay non-prime collections of cells
Carmelo Cisto, Rizwan Jahangir, Francesco Navarra
Communications in Algebra, Vol. 53, No. 9, pp. 3555–3580
5
On Cohen–Macaulay posets of dimension two and permutation graphs
Rizwan Jahangir, Dharm Veer
Bulletin of the Malaysian Mathematical Sciences Society, Vol. 48, Article 133
6
The Intersection Cohomology of a Fan and the Hodge Conjecture for Toric Varieties
Rizwan Jahangir
arXiv:2512.06755
7
Shellable simplicial complex and switching rook polynomial of frame polyominoes
Rizwan Jahangir, Francesco Navarra
Journal of Pure and Applied Algebra, Vol. 228, No. 6, Article 107576
8
BOURBAKI Reading Memo — Set Theory
Rizwan Jahangir, Daisuke Ishii
9
Crazy Abstract Algebra: Kernel Theory
Rizwan Jahangir, Daisuke Ishii
10
Quantum Sudoku 1 — Its Ring-Theoretic and Paradoxical Structure in Terms of Combinatorial Game Theory and ZFC
Kazuyoshi Katogi, Daisuke Ishii, Rizwan Jahangir
11
PolyominoIdeals: A package for Macaulay2 to work with collections of cells
Carmelo Cisto, Francesco Navarra, Rizwan Jahangir
Computer Algebra Software — Macaulay2
AI, LLMs & Scientific Communication
8 itemsExploring how large language models and generative tools change mathematical research and its communication — from AI-assisted proofs to manga as a public interface for computer science.
1
Maximum Formalism, Maximum Humanity: A Modular Architecture for AI-Generated Manga as a Public Interface for Computer Science Research
Rizwan Jahangir, Daisuke Ishii
2
GIGA for Sequential Art: Decoupled Multi-Chain LLM-Diffusion Pipelines with Autonomous Multimodal Linting for Manga Generation
Rizwan Jahangir, Daisuke Ishii
3
Toward Provably Safe Language Models: A Formal Verification Framework for Intellectual Property Protection Using Lean 4
Rizwan Jahangir, Daisuke Ishii
4
The Accessibility Capability Boundary: Operational Limits and Expansion Potential of AI-Generated Browser-Native Accessibility Systems
Rizwan Jahangir, Daisuke Ishii
arXiv:2605.19638
5
Visualizing Abstract Algebra Structures with ChatGPT: Using Intuitive Fruit Emojis for Permutations
Daisuke Ishii, Rizwan Jahangir
6
Pros and Cons of Using ChatGPT for Ring Theory Research
Daisuke Ishii, Rizwan Jahangir
7
Applications of Polyomino Ideals in Daily Life: A Research Memo
Daisuke Ishii, Rizwan Jahangir
8
Leveraging ChatGPT for Advanced Mathematical Research: A Case Study on Polyomino Ideals
Daisuke Ishii, Rizwan Jahangir
Cryptography & Security
3 itemsPost-quantum cryptography through the lens of lattices and combinatorial Hodge theory, and frameworks for communicating security assumptions transparently.
1
Explainable PQC: A Layered Interpretive Framework for Post-Quantum Cryptographic Security Assumptions
Daisuke Ishii, Rizwan Jahangir
arXiv:2604.03665
2
Proof is Beautiful: Bridging Theoretical Rigor and Practical Security
Daisuke Ishii, Rizwan Jahangir
3
Post-Quantum Computing using Knot Theory
Rizwan Jahangir, Daisuke Ishii
Finance & Applied Mathematics
2 itemsInterdisciplinary work connecting group theory, game theory, and PDEs with human behaviour in financial markets.
1
Human-Finance Interaction: An Interdisciplinary Approach to Financial Problems in the Era of ChatGPT, AI and Blockchain
Daisuke Ishii, Rizwan Jahangir
2
Human-Finance Interaction: A Multidisciplinary Approach to Finance Problem Solving in the Era of ChatGPT, AI and Blockchain
Rizwan Jahangir, Daisuke Ishii
Optimization & Systems
7 itemsMathematically grounded design of everyday systems: Kanban workflows, serverless database deployment, time allocation, and neural network architecture.
1
Designing a Stable and Principled Kanban System via Mathematical Policies
Daisuke Ishii, Rizwan Jahangir
2
A Simple Mathematical Boundary for Safe Relational Database Deployment in Serverless Environments
Daisuke Ishii, Rizwan Jahangir
3
Time Allocation Optimization Across Life Roles
Rizwan Jahangir
4
Graph Theory Analysis on Deep Neural Network Architecture
Daisuke Ishii, Rizwan Jahangir
5
Einstein Machine Project: A Hypothesis for a Mass-Production System Supporting All Independent Researchers
Daisuke Ishii, Rizwan Jahangir
6
Braid Computer Architecture: A Hypothesis for Next-Generation Quantum Computers Using Knot and Braid Theory
Rizwan Jahangir, Daisuke Ishii
7
Project "Einstein Machine": A Proposal for Establishing a Mass Production System to Facilitate Research for All Individuals
Daisuke Ishii, Rizwan Jahangir